1. Using Scientific
Measurements

2. Accuracy and Precision
Accuracy is the closeness of measurements to
the correct or accepted value of the quantity
measured.
Precision is the closeness of a set of
measurements of the same quantity made in the
same way (close to one another, but not
necessarily close to accepted value.

3. How are accuracy and precision related?

4. How is accuracy and precision measured?
Percent error is calculated by subtracting the
accepted value from the experimental value,
dividing the difference by the accepted value,
and then multiplying by 100.

5. A student measures the mass and volume of
Sample Problem:
A student measures the mass and volume of
a substance and calculates its density as
1.40 g/mL. The correct, or accepted, value of
the density is 1.30 g/mL. What is the percentage
error of the student’s measurement?
1.40 g/mL -
1.30 g/mL
x 100
= 7.7%
% Error =
1.30 g/mL
Notice that the student’s percentage error is a positive number.

6. What does a positive or negative percentage error mean?
(-) Percent Error – accepted value is greater
than experimental value
(+) Percent Error – accepted value is less than
experimental value
In the sample problem the student’s experimental
value was 1.40 g/mL and the accepted value
was 1.30 g/mL. His percentage error was
positive.

7. Why do (should) we care about percentage error?
Error or uncertainty always exists in any
measurement. The skill of the measurer or
instrument may affect the outcome.

8. Significant Figures Significant Figures in a measurement consist
of all the digits known with certainty plus one
final digit, which is somewhat uncertain or is
estimated.
The term “significant” does not mean certain.

9. Yes!!!!! What value should be recorded for the length of this nail? 6.
What digit should be
recorded first?
Second?
Third?
Yes!!!!! 6. 3 5 cm
Do we need to add a unit?

10. Rules for Determining Significant Zeros
Zeros appearing between nonzero digits are significant.
Example: has 4 significant figures.
Zeros appearing in front of all nonzero digits are not significant.
Example: has 1 significant figure.
Zeros at the end of a number and to the right of the decimal point are significant.
Example: has 4 significant figures.

11. Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just the placeholder, it is not significant. A decimal point placed after zeros indicated that they are significant.
Example: 500 has 1 significant figure
500. has 3 significant figures
500.0 has 4 significant figures

12. Addition or Subtraction with Significant Figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
2 decimal
places
Example: cm cm
3 decimal
places
3.709 cm
answer can
only have 2
decimal places
3.71 cm

13. Multiplication and Division with Significant Figures
For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.
Example: cm x cm = cm2
9.74 cm2
3 significant
figures
5 significant
figures
Round to 3
significant figures